Shock compression process and performance analysis of a two-stage detonation tube with low fill fraction

To investigate the effects of partial fuel filling on impulse and energy efficiency in pulse detonation tubes, experimental and numerical studies were conducted on a two-stage detonation tube with low fill fraction (0.094–0.305). The mechanical energy of the flow field was characterized by pressure exergy and kinetic energy. An approximate treatment was developed to calculate tube exit cross-section impulse based on exhaust flow characteristics of detonation tube with low fill fraction. Results indicate that increase of acoustic relaxation length caused by partial-filled effect leads to a longer exhaust duration (2.5–6 ms in experiments, 3–9 ms in numerical simulations), and the compression process of detonation-driven shock wave can be approximated as piston-driven shock wave. This compression process converts part of the internal energy into mechanical energy during the expansion of high-temperature burnt gas, and the partial-filled effect increases the total mechanical energy efficiency of the flow field. The case with a fill fraction of 0.094 achieved a mechanical energy efficiency increment exceeding 12.0%, with a total mechanical energy efficiency of 39.5%. When the shock front reached the tube end, the pressure exergy of compressed air accounted for 42.4%–58.3% of total pressure exergy, and the kinetic energy of compressed air accounted for 63%–82% of total kinetic energy, indicating most mechanical energy from detonation was transferred to non-combustible gases. Performance analysis revealed that shock attenuation in the diverging section significantly impacts impulse per unit area. The wide overpressure duration created a sonic exhaust plateau (Ma=1) lasting up to 4.1 ms at the exit, substantially reducing the contribution of the pressure term to the force.